Problem Solving

Shalabh's Quants wrote:Dear Mithun,

See this one from Master GMAT.

https://www.beatthegmat.com/mba/2012/04/ ... perts-miss

GMATGuruNY wrote:

mathewmithun wrote:If x/lxl<x, which of the following must be true about x
(Note: Read lxl as modulus x)

A) x>1
B) x>-1
C) lxl<1
D) lxl = 1
E) lxl^2 > 1

An efficient approach is to COMPARE THE ANSWER CHOICES and to plug in values that are included in some ranges but not in others.

A: x > 1
B: x > -1

x=-1/2 is included in the range of answer choice B but not in the range of answer choice A.
Plugging x = -1/2 into x/lxl<x, we get:
(-1/2)/|1/2| < -1/2
-1 < -1/2.
This works.
Eliminate A and any other answer choice that does not include x=-1/2 within its range.
Eliminate A, D and E.

B: x > -1
C: |x| < 1.

x=2 is included in the range of answer choice B but not in the range of answer choice C.
Plugging x=2 into x/lxl<x, we get:
(2)/|2| < 2
1 < 2.
This works.
Eliminate C.

The correct answer is B.

Mo2men wrote:Dear Mitch,

I understood the solution but I have a doubt about Choice B.

Choice B is: X>-1, does it mean that 0 included in the choice B, while X can't be 0 as it will make denominator be 0.

Thanks

mjmehta81 wrote:Hello Mitch,
I do not understand where I am wrong in my understanding below.

For option A.. let x=3, so 3/mod(3)=1. 1 less than 3. This is true for all value of x greater than 1. So why A is wrong option.